A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with i… - G.H. Hardy

A chess problem is genuine mathematics, but it is in some way 'trivial' mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful – important if you like, but the word is very ambiguous, and 'serious' expresses what I mean much better.

A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, [...] the importance of ideas in poetry is habitually exaggerated: '... Poetry is not the thing said but a way of saying it.' [In poetry,] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.

A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.